Small Area Estimation to estimate the number of working and school population

Background

This report aims to estimate the number of working and school population at metropolitan area in Central Jawa called Kedungsepur (Kab Kendal, Kab Demak, Kota Semarang, Kab Semarang, Kota Salatiga, Kab Grobogan). Method used to estimate the number of working and school population is small area estimation. We tried some SAE models and selected a model with the best accuracy

Library loading

library(readxl)
library(foreign)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(ggplot2)
library(reshape2)
library(sae)

## Loading required package: MASS

## 
## Attaching package: 'MASS'

## The following object is masked from 'package:dplyr':
## 
##     select

## Loading required package: lme4

## Loading required package: Matrix

library(tidyr)

## 
## Attaching package: 'tidyr'

## The following objects are masked from 'package:Matrix':
## 
##     expand, pack, unpack

## The following object is masked from 'package:reshape2':
## 
##     smiths

library(haven)
library(survey)

## Loading required package: grid

## Loading required package: survival

## 
## Attaching package: 'survey'

## The following object is masked from 'package:graphics':
## 
##     dotchart

library(stringr)

read data

sae_dataset <- read.csv("selected variables.csv") %>%
  na.omit()
sae_dataset <- sae_dataset %>%
  mutate(var_dir = as.numeric(unlist((RSE * ESTIMATE/100)^2)))

employ SAE EBLUP Fay Herriot
ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + prop_sktm + jml_koperasi

sae_eblup = mseFH(ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + 
                    prop_sktm + jml_koperasi, vardir=var_dir, 
                  method = "REML", MAXITER = 500, PRECISION = 0.0001,
                  B = 0, data=sae_dataset)
mse_eblup = data.frame(sae_eblup$mse)
est_eblup = data.frame(sae_eblup$est$eblup)

eblup <- cbind(est_eblup,mse_eblup) %>%
  rename(est = sae_eblup.est.eblup,
         mse = sae_eblup.mse)
eblup <- eblup %>%
  mutate(CV = (mse^0.5)/est*100)
eblup <- eblup %>%
  mutate(model = "EBLUP")

employ SAE HB under normal distribution
ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + prop_sktm + jml_koperasi

library(saeHB)

## 
## Attaching package: 'saeHB'

## The following object is masked from 'package:stats':
## 
##     Gamma

par(mfrow = c(2,2))   
HB_normal = 
  Normal(ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + 
                    prop_sktm + jml_koperasi,
         vardir = "var_dir",
         iter.update = 100,
         iter.mcmc = 10000,
         thin = 10,
         burn.in = 4000,
         tau.u = 1,
         data=sae_dataset)

## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model
## 
## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 92
##    Unobserved stochastic nodes: 100
##    Total graph size: 1318
## 
## Initializing model

HB_normal_data <- data.frame(HB_normal$Est) %>%
  dplyr::select(MEAN,SD)
HB_normal_data <- HB_normal_data %>%
  rename(est = MEAN,
         SD = SD)
HB_normal_data <- HB_normal_data %>%
  mutate(CV = SD/est*100)
HB_normal_data <- HB_normal_data %>%
  mutate(model = "HB_normal")

Employ SAE HB under beta distribution

#library(saeHB)
#par(mfrow = c(2,2))
#sae_dataset
#HB_beta =
#  Beta(
#  ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + 
#                    prop_sktm + jml_koperasi,
#  iter.update = 100,
#  iter.mcmc = 10000,
#  thin = 4,
#  burn.in = 2000,
#  tau.u = 1,
#  data = sae_dataset)

employ SAE HB under negative binomial distribution

#v= c(1,1,1,1,1,1,1)
#c= c(0,0,0,0,0,0,0)
#HB_negbinomial =
#  NegativeBinomial(ESTIMATE ~ jml_smp + jml_eko + jml_medis + jml_bank + 
#                    prop_sktm + jml_koperasi,
#                  iter.update=1000,
#                  var.coef = v,
#                  coef = c,
#                  data=sae_dataset
#                  )

Employ FH with log transformation

library(emdi)

## Registered S3 method overwritten by 'openxlsx':
##   method               from         
##   as.character.formula formula.tools

## 
## Attaching package: 'emdi'

## The following object is masked from 'package:sae':
## 
##     direct

## The following object is masked from 'package:stats':
## 
##     step

#vars <- c("prop_bts","prop_perdesaan","prop_sd","jml_sd","prop_smp","jml_smp","prop_sma","jml_sma","prop_pt","jml_pt","prop_desaagri","prop_desanonagri","prop_imk","jml_imk","prop_bank","jml_bank","prop_koperasi","jml_koperasi","prop_eko","jml_eko","prop_kredit","jml_kredit","prop_sktm","prop_health","jml_health","prop_skill","prop_blt","prop_padatkarya","prop_kumuh","prop_air","prop_sani","prop_aksesjalan","prop_sinyalinet","prop_medis","jml_medis","prop_angkumum")


#remove_highly_correlated <- function(data, vars, threshold = 0.8) {
#  aux_vars <- vars[sapply(vars, function(v) { x <- data[[v]]; !all(is.na(x)) && sd(x, na.rm = TRUE) > 0 })]
#  datamat <- data[, aux_vars, drop=FALSE]
#  to_remove <- c()
#  repeat {
#    cor_mat <- cor(datamat, use = "pairwise.complete.obs")
#    cor_mat[lower.tri(cor_mat, diag = TRUE)] <- NA
#    max_cor <- max(abs(cor_mat), na.rm = TRUE)
#    if (is.na(max_cor) || max_cor <= threshold) break
#    idx <- which(abs(cor_mat) == max_cor, arr.ind = TRUE)[1, ]
#    v1 <- rownames(cor_mat)[idx[1]]
#    v2 <- colnames(cor_mat)[idx[2]]
#    var1 <- var(datamat[[v1]], na.rm = TRUE)
#    var2 <- var(datamat[[v2]], na.rm = TRUE)
#    if (var1 >= var2) {
#      to_remove <- c(to_remove, v2)
#      datamat[[v2]] <- NULL
#    } else {
#      to_remove <- c(to_remove, v1)
#      datamat[[v1]] <- NULL
#    }
#  }
#  final_vars <- setdiff(aux_vars, to_remove)
#  return(final_vars)
#}


#  candidate_vars_sub <- sae_dataset %>%
#    dplyr::select(!c(X,IDAREA,ESTIMATE,RSE,var_dir))
#  vars_final <- remove_highly_correlated(candidate_vars_sub, vars)
  
#  fh_emdi <- fh(
#    fixed = as.formula(paste("ESTIMATE ~", paste(vars_final, collapse = " + "))),
#    vardir = "var_dir",
#    combined_data = sae_dataset,
#    domains = "IDAREA",
#    MSE = TRUE,
#    transformation = "log",
#    backtransformation = "bc_crude",
#    method = "ml"
#  )
#  step_fh <- emdi::step(fh_emdi, criterion = "AICc", direction = "both")

#print(step_fh$fixed)

fh_model <- fh(
    fixed = ESTIMATE ~ prop_sd + jml_bank + jml_eko + prop_kredit + prop_medis + 
      jml_medis,
    vardir = "var_dir",
    combined_data = sae_dataset,
    domains = "IDAREA",
    MSE = TRUE,
    transformation = "log",
    backtransformation = "bc_crude",
    method = "ml"
  )

FH_logtrans <- data.frame(est = fh_model$ind$FH, MSE = fh_model$MSE$FH)
FH_logtrans <- FH_logtrans %>%
  mutate(CV = (MSE^0.5)/est*100)
FH_logtrans <- FH_logtrans %>%
  dplyr::select(!MSE) %>%
  mutate(model = "FH logtrans")

print(fh_model$fixed)

## ESTIMATE ~ prop_sd + jml_bank + jml_eko + prop_kredit + prop_medis + 
##     jml_medis

the best model for FH with log transformation is as above

summary(fh_model)

## Call:
##  fh(fixed = ESTIMATE ~ prop_sd + jml_bank + jml_eko + prop_kredit + 
##     prop_medis + jml_medis, vardir = "var_dir", combined_data = sae_dataset, 
##     domains = "IDAREA", method = "ml", transformation = "log", 
##     backtransformation = "bc_crude", MSE = TRUE)
## 
## Out-of-sample domains:  0 
## In-sample domains:  92 
## 
## Variance and MSE estimation:
## Variance estimation method:  ml 
## Estimated variance component(s):  4.738746e-05 
## MSE method:  datta-lahiri 
## 
## Coefficients:
##             coefficients   std.error t.value   p.value    
## (Intercept)  11.05949725  0.36903551 29.9687 < 2.2e-16 ***
## prop_sd      -4.37726403  2.15225362 -2.0338 0.0419713 *  
## jml_bank     -0.01292820  0.00598183 -2.1612 0.0306765 *  
## jml_eko       0.00027946  0.00017033  1.6407 0.1008670    
## prop_kredit   5.29906380  3.45361586  1.5344 0.1249430    
## prop_medis   -1.34041281  0.35182254 -3.8099 0.0001390 ***
## jml_medis     0.00396658  0.00101994  3.8890 0.0001006 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Explanatory measures:
##    loglike      AIC      BIC     AdjR2     FH_R2
## 1 -32.0488 80.09761 100.2719 0.5991787 0.9936997
## 
## Residual diagnostics:
##                           Skewness Kurtosis Shapiro_W  Shapiro_p
## Standardized_Residuals -0.12466738 3.564284 0.9792427 0.15000907
## Random_effects         -0.06788717 4.040607 0.9729892 0.05284105
## 
## Transformation:
##  Transformation Back_transformation
##             log            bc_crude

compare_plot(fh_model, CV = TRUE, label = "no_title")

## Press [enter] to continue

## Press [enter] to continue

## Press [enter] to continue

Visualization

direct <- sae_dataset %>%
  dplyr::select(ESTIMATE, RSE)
direct <- direct %>%
  rename(est = ESTIMATE,
         CV = RSE) %>%
  mutate(model = "DIRECT")
all_models <- rbind(dplyr::select(eblup,est,CV,model),dplyr::select(HB_normal_data,est,CV,model),direct,FH_logtrans)


all_models %>%
  ggplot(aes(y = est,
             x = model,
             color = model)) +
  geom_boxplot() +
  theme_bw() +
  theme(legend.position = "bottom",
        axis.text.x = element_blank(),
        axis.ticks.x = element_blank()) +
  ylab("Estimasi jumlah ppd bekerja atau sekolah") +
  xlab("")

all_models %>%
  ggplot(aes(y = CV,
             x = model,
             color = model)) +
  geom_boxplot() +
  theme_bw() +
  geom_hline(yintercept = 25) +
  theme(legend.position = "bottom",
        axis.text.x = element_blank(),
        axis.ticks.x = element_blank()) +
  ylab("CV") +
  xlab("")

all_models %>%
  filter(model== "DIRECT") %>%
  count(CV <=25)

##   CV <= 25  n
## 1    FALSE 91
## 2     TRUE  1

all_models %>%
  filter(model== "EBLUP") %>%
  count(CV <=25)

##   CV <= 25  n
## 1    FALSE  7
## 2     TRUE 85

all_models %>%
  filter(model== "HB_normal") %>%
  count(CV <=25)

##   CV <= 25  n
## 1     TRUE 92

all_models %>%
  filter(model== "FH logtrans") %>%
  count(CV <=25)

##   CV <= 25  n
## 1    FALSE  5
## 2     TRUE 87

Small Area Estimation to estimate the number of working and school population

Dhiar Larasati

2025-05-06

Background